Nonparametric Decomposition of Counterfactual Distributions

Abstract

In this paper, we propose a method to evaluate the effect of a counterfactual change in the marginal distribution of a single covariate on the unconditional distribution of an outcome variable of interest. We show that such effects are point identified for continuously distributed regressors under general conditions, but typically only partially identified if the regressor is discretely distributed. We also discuss estimation and inference for both cases. An implication of our result is that the Oaxaca-Blinder decomposition, which is frequently used in applied work, cannot be generalized to arbitrary nonparametric models except for some special cases.